HLM Questions

#1
I'm trying to get familiar with Hierarchical Linear Modeling (HLM) for my thesis and have some questions. Please answer whatever you can!

I have performance data for 1100 employees (Level 1) nested into 169 supervisors (Level 2). I want to see if certain characteristics of performance (e.g., level of average performance, if the trend is increasing/decreasing) impact annual performance ratings made by supervisors.....

1. There's a range of 1 to 20 employees per supervisor. Since supervisor will be my Level 2 grouping category, does this pose a problem with running HLM if some of the groups are so small with only 1 or 2 employees?

2. The performance data was changed into z-scores in SPSS prior to running HLM. Therefore I'm assuming this means I do not need to center the predictors if 0 is a meaningful value?

3. This question may be a little more complicated. Some of the employees work in busier districts than the others. To control for this I standardized the performance scores within each district so the performance of Jane in busy district A wouldn't be transformed along with Joe in slow district B. However, just because 2 people work in different districts does not mean they will have different supervisors. A supervisor may have employees working in both districts A, B and wherever else. Since I'm grouping employees by supervisor in my HLM analysis, but their scores were transformed into zscores by an overlapping variable (district), does this mean my level 2 groups are violating the independent rule?

I greatly appreciate any insight that may be provided
 

Lazar

Phineas Packard
#2
I'm trying to get familiar with Hierarchical Linear Modeling (HLM) for my thesis and have some questions. Please answer whatever you can!

I have performance data for 1100 employees (Level 1) nested into 169 supervisors (Level 2). I want to see if certain characteristics of performance (e.g., level of average performance, if the trend is increasing/decreasing) impact annual performance ratings made by supervisors.....

1. There's a range of 1 to 20 employees per supervisor. Since supervisor will be my Level 2 grouping category, does this pose a problem with running HLM if some of the groups are so small with only 1 or 2 employees?
It can present a problem yes. There are however different estimators. You might want to have a look at how multilevel modelling is done with diads but, depending on what you want to do, you might have to drop some of these smaller groups.

2. The performance data was changed into z-scores in SPSS prior to running HLM. Therefore I'm assuming this means I do not need to center the predictors if 0 is a meaningful value?
Normally yes. HOWEVER note that this represents a grandmean centering, rarely but for some things you might want to consider group mean centering which case you will have to re-center your variables.

3. This question may be a little more complicated. Some of the employees work in busier districts than the others. To control for this I standardized the performance scores within each district so the performance of Jane in busy district A wouldn't be transformed along with Joe in slow district B. However, just because 2 people work in different districts does not mean they will have different supervisors. A supervisor may have employees working in both districts A, B and wherever else. Since I'm grouping employees by supervisor in my HLM analysis, but their scores were transformed into zscores by an overlapping variable (district), does this mean my level 2 groups are violating the independent rule?
hmm not sure about this approach. Depending on how many districts there are you might want to consider using district as a level 3 group. HLM or MLwiN will both handle cross-classification (employees with same supervisor but in different districts) fairly easily.
 
#3
Lazar, I really appreciate your help. There are 61 districts, which I think may be too small to use as a third level, especially when looking at how many raters from level 2 are in each district.

I was also thinking of using the group mean centering since I want to see how people are rated with respect to their peers performance. That said, I don't necessarily care for an absolute value for the entire sample that says, for example, overall employees with an average performance of 10 units/week are rated more favorably by their supervisors. Instead, I want to use relative comparisons and know if those with above average performance [in comparison to others with the same supervisor rater] are rated more favorably.

I think this would call for group mean centering? I read that I might need to add a Level 2 variable that represents the group mean for each rater too if I go with this method. It just seems so much more complicated than the others :/